a = k/b
6 = k/3 k = proportionality constant = 18
a = 18 / 8 = 9/4 = 2 1/4 when b = 8
z^2 -21z+12 = 0 via quadratic formula z = 21/2 ± sqrt(393) /2
sum = 42/2 = 21 (which is just - b/a)
Here is a picture:
The cotangent function is positive in quadrant III.
The cosecant function is positive in quadrant III.
The cosine function is positive in quadrant I.
The sine function is negative in quadrant II.
The tangent function is negative in quadrant IV.
This equation is a dome shaped parabola maximum will occur at the vertex
the roots of the equation should be = and at the vetex for the max value
this will require that the discriminant = 0
50 > -5x^2 + 20x + c
-5x^2 + 20 x + c-50 < 0
find when discr = 0
20^2 - 4(-5)(c-50) = 0
400 + 20c - 1000 = 0
20c = 600
c = 30 max for fxn to = 50 so c<30
y = -5x^2 +20x + 20
-5 ( x^2 -4) + 20
-5 ( x -2)2 +20 + 20
y= - 5 ( x-2)^2 + 40
You can do part iii
Triangle side length rule sum of two side must be greater than third side
(3+x) > 5 x >2
5+x > 3 x anyhting
5+3 > x
x < 8 values of x can be 3 4 5 6 7 5 possible integer values
11 c 6 = 11! /( 6! 5!) = 462 ways
Charger ! PLEASE post more than just ANSWERS..... we should not be here to just give answers, but rather METHODS to solve the questions....we do not need to provide answers for people's homework so they do and learn nothing ! We aren't really interested in YOUR math abilities...
Thanks, Charger !
s = sum
simple interest amount = s * .05 * 3
coumpound iterst amount s [ (1.05)3 -1 ] difference = 36.60
s [1.053 -1] - s* .05* 3 = 36.60
.157625 s - .15 s
.007625 s = 36.60
s = $ 4800
the point x = k y = k+1 must satisfy the equation
sub in for x and y
k+1 = 4(k) - 14
15 = 3k
k = 5
